Combining multiple Streak variant files with their filename

I am trying to concatenate multiple Strelka vcf files from different samples to one file. Using vcf-concat I was able to combine them. But, I also want to include their sample name/filename in the merged file, preferably as the first column. Is there a way to do that using VCFtools?

Code I used:

vcf-concat File1.vcf.gz File2.vcf.gz File3.vcf.gz | gzip -c > Merged.vcf.gz

Many thanks!

Parvathi.